Question: Solve for $x$ and $y$ using elimination. ${-2x-6y = -20}$ ${2x-5y = -2}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $-11y = -22$ $\dfrac{-11y}{{-11}} = \dfrac{-22}{{-11}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {-2x-6y = -20}\thinspace$ to find $x$ ${-2x - 6}{(2)}{= -20}$ $-2x-12 = -20$ $-2x-12{+12} = -20{+12}$ $-2x = -8$ $\dfrac{-2x}{{-2}} = \dfrac{-8}{{-2}}$ ${x = 4}$ You can also plug ${y = 2}$ into $\thinspace {2x-5y = -2}\thinspace$ and get the same answer for $x$ : ${2x - 5}{(2)}{= -2}$ ${x = 4}$